As other people have already mentioned; in informal or conversational writing, starting a sentence with "And" is fine. That said, the writing style of NKS does not annoy me, because I never got around to reading it!
This thread does remind me, however, of the infamous "Lord" Timothy Dexter.
To quote from: http://en.wikipedia.org/wiki/Timothy_Dexter
"""
At the age of 50 he wrote a book about himself - A Pickle for the Knowing Ones or Plain Truth in a Homespun Dress. He wrote about himself and complained about politicians, clergy and his wife. The book contained 8,847 words and 33,864 letters, but no punctuation, and capital letters were seemingly random. At first he handed his book out for free, but it became popular and was re-printed in eight editions. In the second edition Dexter added an extra page which consisted of 13 lines of punctuation marks. Dexter instructed readers to "peper and solt it as they plese".
""""
Simon